Question

20) Which rule yields the dilation of the figure RSTU centered at the origin?

A)
(x, y) → (4x, 4y)

B)
(x, y) → (0.25x, 0.25y)

C)
(x, y) → (x + 4, y + 4)


D)
(x, y) → (x + 0.25, y + 0.25)

Answer 1

A) (x,y)->(4x,4y) because the x and y values are multiplied by 4 when dilated. Ex. U(-1,1) was dilated to U’(-4,4). -1 was multiplied by 4 to get -4 for the x value and 1 was multiplied by 4 to get 4 for the y value.

Answer 2

Answer: A)
`(x,y)\to(4x,4y)`

Explanation:

The rule of dilating a shape by scale factor k centered at the origin is given by :-

`(x,y)\rightarrow (kx,ky)` [We multiply k to the coordinates of pre-image ]

It means Option C) and D) is incorrect.

From the given graph , it can be observe that quadrilateral R'S'T'U' (image) is larger than the RSTU (pre-image) .

It means the scale factor should be greater than 1. [∵ Scale factor for enlargement is k>1]

Then, Option B is also incorrect.

Hence, the rule yields the dilation of the figure RSTU centered at the origin is given by option A)

i.e.
`(x,y)\to(4x,4y)`